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On a general Maclaurin's inequality


Authors: Stefano Favaro and Stephen G. Walker
Journal: Proc. Amer. Math. Soc. 146 (2018), 175-188
MSC (2010): Primary 26D15, 26C05
DOI: https://doi.org/10.1090/proc/13673
Published electronically: July 20, 2017
Addendum: Proc. Amer. Math. Soc. 146 (2018), 2217-2218.
MathSciNet review: 3723131
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Abstract: Maclaurin's inequality provides a sequence of inequalities that interpolate between the arithmetic mean at the high end and the geometric mean at the low end. We introduce a similar interpolating sequence of inequalities between the weighted arithmetic and geometric mean with arbitrary weights. Maclaurin's inequality arises for uniform weights. As a by-product we obtain inequalities that may be of interest in the theory of Jacobi polynomials.


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Additional Information

Stefano Favaro
Affiliation: Department of Economics and Statistics, University of Torino, Corso Unione Sovietica 218/bis, 10134 Torino, Italy
Email: stefano.favaro@unito.it

Stephen G. Walker
Affiliation: Department of Mathematics, University of Texas at Austin, One University Station, C1200 Austin, Texas
Email: s.g.walker@math.utexas.edu

DOI: https://doi.org/10.1090/proc/13673
Received by editor(s): July 11, 2016
Received by editor(s) in revised form: January 22, 2017
Published electronically: July 20, 2017
Communicated by: Mourad E. H. Ismail
Article copyright: © Copyright 2017 American Mathematical Society